Dual wave-particle' property of electrons

I know that electrons get a dual 'wave-particle' property. I wonder if the velocity of the electrons is different, is that the diffraction pattern in the experiment proving that electrons get wave property differ? Also, is that electron gets a definite wave length and frequency? Is the wave moves with light speed?

In quantum physics, the dynamics of all particles are described by a wave function.
The wavelength of any particle can be found by the de Broglie equation: λ = h/p
If you change the velocity, you change the momentum (denoted as p above).
This will change the wavelength, and therefore change the diffraction pattern accordingly.

The electron is like a bump on a wave … the bump moves at a different speed from the wave. The wave moves faster than light, but that doesn't contradict causality, because the wave itself is uniform, and so carries no information.

If the speed of the electron is v, then the speed of the bump is v, and the speed of the wave is c2/v (so the product of the speeds is c2).

All elementary particles, including the quark, have wave-particle duality.

I wonder if the velocity of the electrons is different, is that the diffraction pattern in the experiment proving that electrons get wave property differ? Also, is that electron gets a definite wave length and frequency?

Click to expand...

The wavelength of a particle depends on its frequency. Different wavelengths have different frequencies: frequency = v/λ = p/mλ.

Just a small(ish) point - it might be OK to think about the electron "surfing" the waveform, but that's a little like the model of the atom that looks like planets revolving around the sun, but smaller. It might do for now - but "wave-particle" duality is much deeper than this. It involves all sorts of philosophical questions.

Let me add to what has already been posted. With respect to shaun_o_kane's "deep philosophical issues":

Electrons are a class of physical process which when we attempt to describe in terms of physical objects can be partially described in terms of particle properties and can partially be described in terms of wave properties. But you must keep in mind that the wave is not the electron it is a mathematical description. The wave is a wave of probability amplitudes and not a physical wave per se. Similarly the point particle is not the electron. The particle's position is the position of an interaction event with the electron not of the electron itself per se.

The nature of physics is that, though we often describe an objective reality, the heart of the physical theory is the behavior of nature not its state. When you push your observations to the level of quantum phenomena then the object/objective state descriptions break down and you must stop thinking in terms of "what is" and stick to "what happens/will happen/has happened/might happen/might have happened..."

Many of the seeming paradoxes in quantum theory are on par with the paradox of dramatically telling someone who just drank poison "you're already dead!". (The paradox being saying "you're dead" implies you're talking to a dead person who thus can't hear you)

Although the statement is worded as a statement about reality it is actually a statement about a process "you are dying" coached in objective terms. In physics it is very hard to get away from such language, we grow up using it, but you have to train yourself to make the distinction.

The electron's wave-function is not the state of the electron, it is a description of what we know about how the electron has/will behave.

I happen to agree with Jim Baugh's description of state and sticking to a probabilistic view of the world. I happen to be of that generation of physicists who were taught Copenhagen as fact, and find it disturbing that the so many now have what I believe is a confused view of QM. Many postings to this forum are clearly from those who would disagree with Jim!

However to suggest that there are no philosophical issues is just wrong. Bohr and Heisenberg spent many hours arguing over them. Feynman said QM is disturbing - and he wasn't just talking about integrals!

I believe that it is a great failing in education that QM philospohical issues are not given the place they deserve. What seems to happen is someone makes up their mind (as Jim has) and then anything else is dismissed. It allows quake-pottery to perist. I'm afraid that, like biologists who need to convince each new generation that Evolution is fact, each new generation of physicist needs to be convinced of Copenhagen. And Copenhagen is far more subtle than just wave-particle duality.

How can Physics advance without philosophy? Einstein's brilliance in part was that he did think philosophically. Perhaps Jim does not believe in Copenhagen, just mathematical models? These days, I work in an investment bank. I don't trust models without understanding the assumptions that went into them. Neither should anyone else.

Staff: Mentor

It's not a black and white choice between the Copenhagen interpretation and "just mathematical models." There are other interpretations of QM besides Copenhagen. Around here, being dogmatic about interpretations is a great way to start an argument.

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Actually, where do the answers of my questions go?

I partly understand what you are talking about. So subtle. What we can do in Physics is only to find in what way it influences other things, am I right? That's why we have to give up the thought of what it is. Maybe there is a machine in invest in what an eletron is, what we can find is only in what way the electron is influencing the machine?

So confused, I clearly understand a little bit of quantum Physics, I need to learn more about it.

Let me clarify a point about my views. I accept the Copenhagen "interpretation".

I believe that the semantic definition of "interpretation" for a scientific theory is how the formal language translates to operational actions in the lab. In short what the theory predicts is it's interpretation.

For quantum theory the interpretation is the Born probability formula along with the various mappings between operators, bras, and kets, and the physical devices in the laboratory to which they correspond.

(Note that the mode vector for e.g. a vertically polarized photon refers not to the photon but to a source of vertically polarized photons. Calling it a mode vector rather than state vector emphasizes that it refers to the mode of preparation and not the photon itself.)

This with Occam's razor dictates the Copenhagen interpretation since "underlying reality" beyond the outcomes of experiments is operationally meaningless.

Other attempts to "interpret" are attempts to re-interpret in classical objective terms what is fundamentally non-classical and non-objective.

From this perspective then any description of reality is "only a model" and thus so too are the various "interpretations" of QM. They should IMNSHO be refered to as "Many-Worlds Model", "Bhom Pilot Wave Model" etc.

I don't want to rehash old arguments here, just respond to statements about my position. If anyone wants to discuss this further I'm game... we can start a new thread.